Introduction

This cell creates an array of cantilevers that have varying lengths. Cantilever, or singly supported beams, can be used for
two tests. First, cantilevers can be used to test the maximum release length. Second, cantilevers can be used to measure the
non-uniform residual stress.

Theory

Peeling Number

The peeling number is a ratio of the elastic energy to the adhesion energy, and can be used to predict whether or not a cantilever
will stick to the substrate once in contact [1,2]

(1)Np=3Et3h2/8γl4

Above, E is Young's modulus, t is the cantilever's thickness, h is the height of the cantilever from the substrate, γ is the energy of adhesion per unit area, and l is the length of the cantilever.

When the peeling number is greater than 1, the cantilever will peel from the substrate, and so not stick to the sruface.
However, if the peeling number is greater than 1, this indicates that the minimum energy configuration includes some portion
of the cantilever stuck to the surface.

Elastocapillary Number

Similar to the peeling number described above, there is the elastocapillary number [3], which is a compares the elastic energy of the cantilever to the adhesion force due to a liquid droplet between the cantilever
and the substrate.

(2)NEC=8EIh2/3γcos(θ)(w+t)l4

Two parameters were introduced: I is the bending moment of inertia, and θ is the contact angle of the liquid.

Parameters

Any parameter may be modified, if necessary, to meet design rules. Typically, this involves increasing parameters that specify
distances, so that minimum line width and minimum line spacing rules will not be violated. This has been extended to the
convention of specifying a zero for some parameters to obtain an instance of the minimum size.

In addition to the parameters listed below, several technology parameters also influence the implementation of parameterized
cells. This data must be present in the technology library.

Table 1: Parameters for the 'cantilevers' parameterized cell.

Name

Description

Range

Units

P1

P2

length_min

The length of the shortest cantilever.

[0,∞)

um

+

+

length_max

The length of the longest cantilever.

[0,∞)

um

+

+

length_step

When creating the array, this parameter determines the difference in cantilever lengths.

[0,∞)

um

+

+

width

This parameter determines the width of the cantilevers. If this value is less then the nominal width it will be increased.

[0,∞)

um

+

+

anchor

The size of the anchors used to connect the cantilevers to the substrate. If this value is less then the nominal width
it will be increased.

[0,∞)

um

+

+

include_poly0

If true, a POLY0 ground plane will be included in the cell. The POLY0 ground plane can eliminate most electrostatic
attraction between the cantilevers and the substrate bulk.